PRODUCTION SCHEDULING OF CONTINUOUS FLOW LINES: MULTIPLE PRODUCTS WITH SETUP TIMES AND COSTS

The problem of production planning and setup scheduling of multiple products on a single facility is studied in this paper. The facility can only produce one product at a time. A setup is required when the production switches from one type of product to another. Both setup times and setup costs are considered. The objective is to determine the setup schedule and production rate for each product that minimize the average total costs, which include the inventory, backlog, and setup costs. Under the assumption of a constant production rate, we obtain the optimal cyclic rotation schedule for the multiple products system. Besides the decision variables studied in the classical economic lot scheduling problem (ELSP), the production rate is also a decision variable in our model. We prove that our solutions improve the results of the classical ELSP.     

Multi-objective scheduling of two-job families on a single machine

This paper presents a preliminary analysis of the typical scheduling environment in semiconductor manufacturing involving multiple job families, and where more than one objective such as cycle time, machine utilization and the due-date accuracy needs to be simultaneously considered. In this study, the NP-hard problem of scheduling N independent jobs on a single testing machine with due dates and sequence-dependent setup times is addressed, where the multiple objectives are to minimize average cycle time, to minimize average tardiness, and to maximize machine utilization. A Pareto optimal solution, which is not inferior to any other feasible solutions in terms of all objectives, is generated combining the analytically optimal and conjunctive simulated scheduling approach. First, the machine-scheduling problem is modeled using the discrete event simulation approach and the problem is divided into simulation clock based lot selection sub-problems. Then, a Pareto optimal lot is selected using the compromise programming technique for multiobjective optimization at each decision instant in simulated time. With the help of a broad experimental design, this developed solution is then compared with common heuristic-dispatching rules such as SPT and EDD, which show better results for all the objectives over a wide range of problems. The developed scheduling method shows approximately 16.7% reduction in average cycle time, 25.6% reduction in average tardiness, and 21.6% improvement in machine utilization over the common dispatching rules, SPT and EDD.     

How Inventory Cost Influences Introduction Timing of Product Line Extensions

In the industry with radical technology push or rapidly changing customer preference, it is firms' common wisdom to introduce high‐end product first, and follow by low‐end product‐line extensions. A key decision in this “down‐market stretch” strategy is the introduction time. High inventory cost is pervasive in such industries, but its impact has long been ignored during the presale planning stage. This study takes a first step toward filling this gap. We propose an integrated inventory (supply) and diffusion (demand) framework and analyze how inventory cost influences the introduction timing of product‐line extensions, considering substitution effect among successive generations. We show that under low inventory cost or frequent replenishment ordering policy, the optimal introduction time indeed follows the well‐known “now or never” rule. However, sequential introduction becomes optimal as the inventory holding gets more substantial or the product life cycle gets shorter. The optimal introduction timing can increase or decrease with the inventory cost depending on the marketplace setting, requiring a careful analysis.     

Risk-averse and risk-taking newsvendors: a conditional expected value approach

Introduction  We consider a company sourcing a product with short life cycle to stock using the framework of the newsvendor model. Traditionally, risk-neutral inventory managers are considered optimizing the expected cost or profit. But experimental findings state that the actual quantity ordered deviates from the optimal quantity derived from the classical newsvendor model. Model  Recently, the newsvendor model with objectives different from maximizing expected profit has been an active field of research. Here, we propose a newsvendor model where the inventory manager can control internal and customer-oriented performance measures. The objective function is a convex combination of conditional expected values of low and high profits, respectively. Results   We give a qualitative characterization of the optimal order quantity and the resulting performance measures in dependence of the model parameters. A risk-averse inventory manager cannot Pareto-dominate a risk-neutral or risk-taking inventory manager with respect to the expected profit and the level of product availability. Finally, the risk preferences of the inventory manager are expressed as a function of the profit value of the product with respect to the level of product availability and the probability of loss, respectively.      

经济批量排产问题的一种排产方法

针对经济批量排产问题假定生产可以在库存降为0之前开始,并且提出新的算法求产品的生产顺序。结果表明,该排产方法成本要低于其他2种常用的经济批量排产问题的方法,并且给出了算法的时间复杂性。     

Centralized inventory in a farming community

A centralized inventory problem is a situation in which several agents face individual inventory problems and make an agreement to coordinate their orders with the objective of reducing costs. In this paper we identify a centralized inventory problem arising in a farming community in northwestern Spain, model the problem using two alternative approaches, find the optimal inventory policies for both models, and propose allocation rules for sharing the optimal costs in this context.     

Inventory Management for Customers with Alternative Lead Times

It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.     

An Analysis of Dual‐Kanban Just‐In‐Time Systems in a Non‐Repetitive Environment

Recent advances in approaches and production technologies for the production of goods and services have made just‐in‐time (JIT) a strong alternative for use in intermittent and small batch production systems, especially when time‐based competition is the norm and a low inventory is a must. However, the conventional JIT system is designed for mass production with a stable master production schedule. This paper suggests supplementing the information provided by production kanbans with information about customer waiting lines to be used by operators to schedule production in each work‐station of intermittent and small batch production systems. This paper uses simulation to analyze the effect of four scheduling policy variables—number of kanbans, length of the withdrawal cycle, information about customer waiting lines, and priority rules on two performance measures—customer wait‐time and inventory. The results show that using information about customer waiting lines reduces customer wait‐time by about 30% while also reducing inventory by about 2%. In addition, the effect of information about customer waiting lines overshadows the effect of priority rules on customer wait‐time and inventory.     

Implementation of holonic scheduling and control in flow-line manufacturing systems: die-casting case study

The success of a flow-line manufacturing system depends on effective production scheduling and control. However, it has been found that current flow-line manufacturing scheduling and control algorithms lack the flexibility to handle interruptions or resource breakdowns; hence, system performance drops automatically and rapidly when interruptions occur. The objective of this research is to investigate if the performance of a flow-line manufacturing system can be improved by integrating agent-based, holonic scheduling and production control. A holonic manufacturing scheduling model has been developed and implemented into a die-casting manufacturing flow line throughout a simulation model. The analysis takes into account the comparisons of overall performances of the system models with the holonic scheduling and conventional scheduling approaches. Simulation results indicate that the holonic manufacturing scheduling and control can significantly increase the uptime efficiency and the production rate of the flow-line manufacturing system.     

带工期指派的产品服务系统订单随机调度问题研究

针对由一个制造工厂和多个区域服务中心组成的服务型制造企业，研究了考虑生产时间和服务时间均具有随机性且工期可指派的产品服务系统（PSS）订单调度问题。首先以最小化订单提前、误工和工期指派费用的期望总额为目标构建问题的优化模型，然后分析目标函数近似值的最优性条件，据此提出加权最短平均生产时间排序规则，并结合该规则与插入邻域局部搜索设计了启发式算法对问题进行求解，最后通过数值仿真验证算法的可行性和有效性。研究表明，提前费用偏差对PSS订单调度与工期指派决策的影响很小，因此企业管理者无需准确估计库存费用也能制定出比较有效的PSS订单调度策略；而工期指派费用偏差对决策结果的影响非常大，因此企业管理者在决策时必须谨慎估计该项费用。     

Coordinated scheduling of production and delivery stages with stage-dependent inventory holding costs

This paper considers a problem of integrated decision-making for job scheduling and delivery batching wherein different inventory holding costs between production and delivery stages are allowed. In the problem, jobs are processed on a facility at a production stage and then delivered at the subsequent delivery stage by a capacitated vehicle. The objective is to find the coordinated schedule of production and delivery that minimizes the total cost of the associated WIP inventory, finished product inventory and delivery, where both the inventory costs are characterized in terms of the weighted flow-time and the delivery cost is proportional to the required number of delivery batches. It is proved that the problem is NP-hard in the strong sense. Thereupon, three heuristic algorithms are derived. Some restricted cases are also characterized as being solvable in polynomial time. Numerical experiments are conducted to evaluate the performance of the derived heuristic algorithms.     

基于新产品的供应链最优生产策略

商业竞争与技术进步导致产品生命周期的缩短,要求企业能不断地推出新产品。而新产品的生产与需求是一个逐步适应和熟悉的过程,具有明显的学习效应。本文运用Bass模型来描述新产品的需求扩散效应,建立了新产品供、产、销三级供应链的生产存储优化模型,并通过算例,计算机模拟出最优生产批量。该研究改进了传统的一般产品的生产存储计划,对面向市场需求的供应链的新产品投产具有重要的指导意义。     

时变供需下基于商业信用的零售商最优订货策略

论文在时变供需环境下,即市场需求为斜坡式时间函数及补货率依赖于市场需求情境下,探讨了基于商业信用的供应链中零售商最优订货策略。首先,根据商业信用期和零售商补货周期的关系,分两种情形构建了零售商库存模型;其次,根据零售商的库存模型,证明了其最优解的存在,并给出相关的命题和算法来求解零售商的最优库存策略;最后,通过数值算例和灵敏度分析来论证文中的有关结论。研究发现:当供应商给予零售商的商业信用期较短时,此时市场需求仍处于增长期,随着市场需求稳定时间点的增大,零售商的最优订货周期逐渐减小,最优订货量和年费用也逐渐减小;当供应商给予零售商的商业信用期较长时,此时市场需求已趋于稳定期,随着市场需求稳定时间点的增大,零售商的最优订货周期逐渐增大,最优订货量和年费用也逐渐增大;当供应商生产与市场需求依赖性逐渐增大时,零售商的最优订货周期逐渐增大,最优订货量及年费用也逐渐增大。     

Lot sizing and scheduling: a survey of practices in Brazilian companies

The lot sizing and scheduling (LSS) problem has motivated much research in production planning and control. However, while there are many papers on modelling this problem, there is scant research on how it is addressed in the industry. We present a survey of Brazilian industry practices in LSS, intending to understand the problem faced by operations managers, drawing parallels with academic findings to identify gaps between theory and practice and opportunities for future research. We confirm that the main objective of practitioners in companies operating under MTS strategy is to maximise service level, followed by inventory reduction. Availability of raw material, demand uncertainty and safety stock levels, lack of decision support software and the impact of sequence-dependent set-up times are other major concerns highlighted by the practitioners. Lastly, we confirmed that despite the relevant body of research on this problem, there is still a large gap between theory and practice.     

冷轧生产批量计划与调度问题模型及算法

对冷轧生产系统特点进行分析,将冷轧生产批量计划与调度问题抽象为多阶段、多品种带有中间库的批量计划与调度问题。针对该问题建立了数学模型,通过对库存成本和调整成本惩罚系数的控制可以协调库存水平和调整次数的关系。对所建立的模型,提出了基于二进制粒子群优化与局部搜索的混合求解算法。最后,通过对企业实际生产数据的计算和分析,验证了模型和算法的可行性和有效性。     

Determination of economic production quantity in a multi-stage production system

In this paper two models have been suggested for determining economic production quantity in a multi-stage production system. The demand for the product is assumed constant and it is supplied by manufacturing the product in equal production runs. The production lot is transported in a number of sub-batches of equal sizes. Each sub-batch is processed on the production stages without wait during process. As a result of processing the sub-batches without wait during process, the processing on the production stages is interrupted. Expressions have been derived for the manufacturing cycle time, the total process inventory and the finished product inventory and then total variable cost models have been suggested and manipulated for obtaining the economic production quantity.     

Optimal price,warranty length and production rate for free replacement policy in the static demand market

In the present paper, a decision model is developed for producers in the static demand market to determine the optimal price, warranty length and production rate of a product to maximize profit based on the pre-determined life cycle. The free renewal warranty policy is considered under which failed products are renewed before the end of warranty length at no cost to consumers. The expected number of renewals based on warranty length is derived for Weibull life distributed products. The objective function includes both demand and cost functions, where production cost, warranty cost and inventory cost are involved. A solution approach using the maximum principle is described, and is applied to two specific cases of markets. The first case of market considers positive discount rate, and the second case of market considers zero discount rate. The economic sensitivity analysis is conducted to evaluate the effect of model parameters on the optimal solution. Some conclusions are drawn based on the sensitivity analysis.     

Simple policies in the economic lot scheduling problem with zero setup costs

The economic lot scheduling problem is analysed for the case when the cost of setups, but not their duration, is assumed to be zero. This would be the case when setups are performed by the machine operators, or when management's goal is holding-cost reduction. Theoretical results are presented describing when the common cycle solution of producing one lot of every item every cycle is optimal or near optimal. Computational results using simulated data are then presented which show that the common cycle solution is nearly optimal in a wide range of practical situations.     

Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs

We develop a new, unified approach to treating continuous‐time stochastic inventory problems with both the average and discounted cost criteria. The approach involves the development of an adjusted discounted cycle cost formula, which has an appealing intuitive interpretation. We show for the first time that an (s, S) policy is optimal in the case of demand having a compound Poisson component as well as a constant rate component. Our demand structure simultaneously generalizes the classical EOQ model and the inventory models with Poisson demand, and we indicate the reasons why this task has been a difficult one. We do not require the surplus cost function to be convex or quasi‐convex as has been assumed in the literature. Finally, we show that the optimal s is unique, but we do not know if optimal S is unique.